Design of inverse permutations derived by compositions of permutations
Daisaburo Yoshioka, Yuuki SAITO · Nonlinear Theory and Its Applications IEICE · 2022
In block encryption algorithms, random permutations are often employed for nonlinear transformation called a substitution box (S-box). Because an S-box is the only nonlinear portion of a block cipher, it accounts for most of implementation costs. For decryption, the circuit implementation of the corresponding inverse permutation is also required. To reduce the circuit size of the inverse permutation, we derive a method to generate inverse permutations based on the compositions of permutations. The effectiveness of the proposed method in terms of the complexity of Boolean functions is demonstrated through its application to the S-box used in PRESENT and to the optimum S-boxes.